Optimum surface contour for conductive heat transfer with a thin flexible workpiece

ABSTRACT

Conductive heat transfer between a thin deformable workpiece and heat sink is optimized by imposing a load over the workpiece resulting in a uniform contact pressure distribution in said workpiece which is also the maximum stress consistent with the elastic properties of the workpiece. The surface of the heat sink is given a contour determined by these criteria for a thin circular disk clamped thereto.

This application is a continuation of application Ser. No. 381,668,filed May 25, 1982, now abandoned.

DESCRIPTION FIELD OF THE INVENTION

The invention is related to heat transport involving objects and thermalreservoirs, and in particular, to cooling of semiconductor waferssubject to processing by ion implantation, sputtering or like processes.

BACKGROUND OF THE INVENTION

In processing steps wherein the workpiece is subject to a high intensityradiation flux, heat developed in the workpiece may become a limitingfactor for the process. In particular, for ion implantation ofsemiconductor materials, an upper limit on the workpiece temperature isrecognized for several reasons. Where the wafer is coated with a resistlayer as part of a lithographic process, deterioration or alteration ofthat layer will occur for temperatures elevated much in excess of 100°C. Wafers subject to prolonged irradiation may also experienceundesirable diffusion of previously formed regions of distinctincremental properties within the semiconductor or a premature annealingof previously bombarded regions may occur.

It is therefore a matter of importance to provide for the removal fromthe semiconductor wafer of heat developed therein consequent to ionimplantation processes or like irradiation.

It is known in the prior art to provide active cooling for semiconductorwafers during ion implantation by clamping such wafers to a convexlycurved platen which includes a coating of a pliable thermally conductivematerial on the surface of the platen. A clamping ring cooperating withthe platen is arranged to firmly press a semiconductor wafer against thecompliant surface of the convexly curved platen to facilitate a thermalenergy transfer from the wafer to active cooling means provided withinthe platen. Such a system is described in U.S. Pat. No. 4,282,924commonly assigned with the present invention.

The aforementioned art relies upon a conductive mechanism for thermaltransport. Thermal energy is developed in proximity to the outer surfaceof the wafer from the kinetic energy of the incident beam which isabsorbed by the wafer. There is, therefore, a first component of thermalconductivity implicit in the thermal conductance properties of the wafermaterial because of the necessity of heat transport through the wafermaterial. (It will be assumed for simplicity that the thermal path isthrough the thickness of the wafer.) Similarly, the platen exhibitsthermal conductance properties characteristic of the material comprisingthe platen in effecting heat transfer between the surface of the platenin contact with the wafer, thence through the interior regions of theplaten wherein cooling channels are disposed for circulating coolingfluids. In the intermediate contact region between the wafer and theplaten there is a distinct contribution to thermal transfer properties.The thermal conductance in this region is nearly proportional to theactual contact area between the wafer and platen and inverselyproportional to the mean thermal conductivity of the two materials. Onthe microscopic scale, the surfaces are quite nonplanar and of irregularorientation; on the basis of certain assumptions of the hardness ofmaterials and surface topography distributions of the respective contactsurfaces, the contact area is calculable for microscopic measurement andis, in fact, but a small fraction of the macroscopic area. The theory ofconductive heat transport between solid bodies in a vacuum is developedby Cooper, Mikic and Yovanovich, Int. J. Heat and Mass Transfer, Vol.12, pp. 279-300 (1969) where it is shown that the contact thermalconductance depends upon the conductances and the actual contact areawhich in turn depends upon the surface density of deviations fromplanarity of the meeting surfaces and the elastic or plastic complianceof the materials. Irregularities may, by impressed forces bearingthereon, be deformed to initially contact, or to more nearly conformwith one another, e.g., yielding a greater contact area. The desirableeffect of greater contact area is limited by the maximum stress whichcan be sustained by the wafer. In U.S. Pat. No. 4,282,924 the platen isin fact a composite of a high heat capacity metal body, of unspecifiedconvex curvature, to which is bonded a thermally conductive compliantouter layer for contacting the wafer. Thus, there is provided a surfacelayer which deforms to accommodate some portion of the small scaleirregularities of the wafer. There is, in this example, a furthergeometrical attribute in the length of the thermal path through thecompliant material, which length is proportionately shortened as thecontact pressure increases. This effect appears in first order but isquite small for the small deformations usually encountered.

The effect of variables which influence the thermal impedance of theinterface was recognized as providing a selectably controllable thermalimpedance where it is desired to sustain a preselected wafer temperaturerelative to the heat sink. U.S. Pat. No. 4,453,080, commonly assigned,discusses an example of this attribute.

It is therefore an object of the present invention to provide anapparatus for improving the effective cooling of semiconductor wafersduring ion implantation and especially with respect to the uniformity ofsuch cooling.

SUMMARY OF THE INVENTION

An apparatus for improved heat transfer for semiconductor wafers subjectto a radiation flux includes a platen to which the wafer is clamped,preferably at the periphery thereof. The platen is given a contour whichoptimizes the heat transfer through the wafer to the platen independentof location on the surface of the wafer. The contour to which the waferconforms on the platen is computed to correspond to that surface forwhich the contact pressure distribution between the wafer and platenwill be uniform over the remaining surface of the wafer for the boundaryconditions specified by the clamping means which secures the wafer tothe platen. The magnitude of the contact pressure is maximized to themagnitude which can be tolerated by the wafer without fracture of thelatter.

In one embodiment the platen comprises a rigid metal member and acompliant layer bonded thereon. The properties of the compliant layerand this inner contour of the member at the bonding surface control anouter effective contour which meets the above-stated requirement.

In either approach, the platen preferably includes active cooling meansfor efficiently removing heat therefrom.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a typical ion implantation systemincluding the present invention.

FIG. 2A is a schematic illustration of a nonoptimally contoured platenand wafer clamp thereon.

FIG. 2B illustrates the effect of the present invention.

FIG. 2C shows another embodiment of the invention.

FIG. 3 illustrates an alternate clamping embodiment.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

The context of the present invention is best described with the aid ofFIG. 1 which illustrates a typical ion implantation system. A highvoltage terminal 2 is maintained at a selectable potential of +10 kev to+200 kev, typically, with respect to ground. Within the terminal 2 thereis located an ion source 8 and associated power supplies 10, providingextraction, probe and focusing potentials which need not be consideredin detail for the present purposes. Typically the ion source operates ona gaseous feed stock requiring gas handling system 6 which may beemployed to select among several gas cylinders and to supply theselected gas to the ion source through a controlled leak. A high currention beam 18 diverging from the ion source 8 is momentum analyzed inanalyzer magnet 20 and issues from the magnet defined by aperture 22 andfurther limited by variable slit system 24. The beam is then acceleratedto ground potential in accelerating tube 26. Optical elements 28 such asa quadrapole doublet, operate on the beam to yield a spatial momentumfocus at the target planes 56 or 58. The typical system of FIG. 1utilizes an electrostatic deflection system including y deflectionplates 40 and x deflection plates 42 to direct the beam 18 over theselected target plane. The waveforms are developed in scan system 44 forapplication to the plates 40 and 42 to achieve a desired scanningpattern. A dual channel target chamber 46 is provided to house theworkpiece(s) subject to processing. Included in the target chamber arebeam defining slits 48 and 49 for the respective processing channels andFaraday cages 50 and 51 for charge collection and integration. Anautomatic wafer handling system including feed channels 52 and 54service the two processing channels for introducing semiconductorwafers, one at a time through each of two vacuum locks for timestaggeredintroduction into the target chamber. The wafer handling system properlylocates, aligns, and cools the wafer during processing and removes theprocessed wafer from the chamber at the conclusion of processing. Thewafer handling system is described in U.S. Pat. No. 4,449,885 commonlyassigned with the present invention.

It is understood that the entire region traversed by the ion beam ismaintained at high vacuum, e.g., typically pressures of the order of10⁻⁶ mm.hg.

It is observed that, as in FIG. 2A, clamping force L applied at theperiphery of the wafer 62 may result in a non-uniform distribution ofcontact forces over the surface of the wafer. This results in anon-uniform loading of the wafer where the load is defined by the platen64 of arbitrary convex surface contour 65. The local stress isrepresented symbolically by stylized vector components 66, one of whichis so labeled. The thermal conductance of the interface between wafer 62and platen 64 is a function of the contact force exerted on the waferagainst the platen and the thermal and mechanical properties of thematerials. As described above, this is due in part to the microscopicsurface roughness and compressibility of the microscopic materialfeatures of both wafer and platen and the resulting contact area of therespective materials which may vary in proportion to the applied force.In a typical peripherally clamped wafer cooling platen of convexspherical shape as in FIG. 2A, it is found that a region of relativelyelevated temperature generally develops in the central region of thewafer during processing due to a decrease in the local contact pressure.

An optimum platen profile follows from derivation of the equation whichdescribes a uniformly loaded thin disc supported along its periphery.This problem is discussed by Marguerre and Woernle, "Elastic Plates",Chapter 11, Blaisdell Publishing Co., Waltham, Mass., 1969. From thisreference one can derive an expression for the deflection y(r) for auniformly loaded peripherally supported thin flexible disc in order toobtain ##EQU1## where r=radial position

D=2r₀, the wafer diameter

t=wafer thickness

p=pressure applied to wafer.

E=elastic modulus

ν=Poisson's ratio

The deflection described by equation (1) above fulfills one criteria foroptimized contact cooling perceived in this work, e.g., uniform contactpressure distribution applied to the wafer. In order to maximize heattransport from the wafer to the platen, it is further desired tomaximize the contact force between the wafer and the platen. Limits areimposed on the maximum contact force by properties of the wafermaterial. As the wafer is deformed against a convex surface, thetangential stress components (tangential with respect to the normalcontact forces) place the wafer under compression near its inner surfaceand under tension near its outer (convex) surface due to imposedbending. The respective surface tangential stress components exhibit amagnitude which delimit the design parameters, (especially the tensilestress at the outer surface).

For a thin uniformly loaded flexible disc the maximum surface stressesresulting from this imposed deflection are given by ##EQU2## and themaximum pressure is limited by the maximum tensile stress to which thewafer is safely subject as ##EQU3## where p=contact pressure

ν=Poisson's ratio

δ=tensile stress on outer surface

δ_(max) =maximum tensile stress tolerable

and r₀ and t are as given above.

It can also be shown that for the thin uniformly loaded flexible disc ofequation 2, the maximum deflection is given by ##EQU4##

A dimensionless expression is formed by dividing equation 1 by equation3 which describes the desired contour for the platen. ##EQU5## Equation4 therefore expresses the concurrent conditions which yield uniformityof heat transfer over the surface of the wafer and maximum heat transferfrom the wafer. It is noted that equation 4 has no dependence on Young'smodulus and that Poisson's ratio varies little within a wide class ofmaterials. Equation 4 expresses a uniformly applicable contour for theproposed purpose. In actual use the value of Y_(max) imposes aconstraint on the amplitude or scale of the curve, but it is noted thatagain a variety of different wafer materials may be accommodated withoutsubstantial sacrifice of thermal transfer properties.

Thus, in FIG. 2B, the platen 70 of the present invention has a surfacecontour 71 described by equation 4. The wafer 72 is urged against theplaten 70 by peripheral clamping ring 74 under a clamping force L.Cooling channels 76 are provided in the platen for the further removalof heat. The stress distribution represented symbolically by vectorcomponent 78 is observed to be uniform over the wafer as a result of theboundary condition of peripheral clamping and the uniform contactpressure loading imposed by conformance of the wafer 72 with the contour71. For the magnitude of contact force L_(o) for which contact isachieved over the entire wafer surface the contact pressure will assumea value which does not change for further increase in L. Furtherincrease in contact force ΔL is simply transmitted through the wafer tothe substrate without affecting the distributed load.

In another embodiment (FIG. 2C) the platen assembly may comprise a rigidmember 80 and a compliant thermally conductive coating 82. Theintermediate contour 90 of the rigid member 80 is determined taking intoconsideration the properties of the compliant material 82 and the loadto which the wafer 86 will be subject in order that the interfacecontour 84 between wafer 86 and platen 80, under the design loadconditions, will conform to that desired contour yielding a contactpressure distribution which is uniform over the surface of theplaten-wafer interface for the boundary conditions determined by theclamping of the wafer to the platen. In the most straight forwardapproach the compliant layer exhibits a uniform thickness bonded to theintermediate contour 90 with the result that the interface contour 84and intermediate contour 90 will be substantially identical. In thegeneral case a compressed compliant layer may exhibit a radial thicknessdistribution due to increased perimeter loading, requiring a complexdesign procedure. Such design is most easily accomplished by aniterative procedure in a computer model for which the function y₁ (r,θ)representing intermediate contour 90 of the bare platen is varied toyield the desired outer contour, y₀ (r,θ), taking account of thedeformation of the compliant layer 82. For a boundary conditionprescribed by continuous peripheral clamping, the θ dependence vanishesand these functions have radial symmetry.

For typical silicon wafers of production dimensions (100 mm. diameterand 525 microns thickness) a tensile bending stress of 8000 psi istolerable. A maximum deflection of 0.0529" is taken as the amplitude ofthe contour given by equation 4. A contact pressure of 0.67 psi ismaintained against an aluminum (6061-T6) heat sink so contoured. Thethermal contact resistance is found to be about 65° C./watt/cm² invacuum. In a specific instance, the aluminum platen body, the compliantsubstrate and the typical wafer contribute, respectively, 0.31, 2.11 and0.033°-0.074° C./watt/cm². As expected the contact impedance, is thedominant contribution to the total thermal impedance, but the actualvalue of the thermal contact resistance is quite dependent upon thesurface properties of the heat sink and wafer. Soft aluminum or indiumare believed to offer excellent properties for this purpose. Pliablematerials offer good properties with the possible advantage oftolerating surface dust.

In a related aspect of the invention, a gas is introduced within thewafer-platen interface region to a pressure approximately equal to thecontact pressure for enhanced heat transfer. This subject material isdescribed in U.S. Pat. No. 4,457,359 commonly assigned.

Alternate clamping arrangements may also be considered. One suchalternate clamping arrangement will apply equal clamping forces L to thewafer at discrete points symmetrically disposed, as shown for example inFIG. 3, at three points equally spaced along the periphery of the wafer.In this instance a complex saddle-shaped contour will result. That is,the wafer will be deformed with a surface y(r,θ) where θ is theazimuthal angle around the periphery. Such a surface may be computedwith reference to Marguerre and Woernle, above referenced. The platen108 is provided with such a saddle-shaped contour further constrained bythe maximum deflection condition. The achievement of the complex contourrequired may readily be obtained using modern multiple axis machiningtechniques. Alternatively the platen 108 may be so formed as in theafore described embodiment with a compliant layer to facilitate thedesired contour with the more complex computations so required. Anadvantage obtained in this discrete clamping embodiment is theadditional wafer area accessible for production of devices on the wafer.The fractional surface area given over to a continuous peripheral clampof width w is ##EQU6## which is of the order of a few percent fortypical values of w(2 mm.) and r_(o). This embodiment is the subject ofU.S. Pat. No. 4,458,746.

Although the discussion has been directed to obtaining a uniform contactpressure between the wafer and a heat sink member, it is clearlyunderstood that another desired distribution can be obtained in likemanner. For example, a temperature gradient may be desired forparticular processing steps other than the examples discussed and thecorresponding contact force distribution may be obtained by appropriatedesign of the contact contour.

The discussion has been framed in the context of removal of heat from asemiconductor wafer during ion implantation. One will readily recognizethat ion implantation is but one form of radiation processing for whichthe invention is well suited. Moreover, the conductive transfer of heataway from thin flexible discs is closely related to the conductivetransfer of heat into such materials; therefore, processes directed toheating a thin flexible workpiece would similarly benefit from theinvention. While the discussion has employed a thin flexible disc as anexample, the invention could be applied to a workpiece of other thancircular symmetry or of non-uniform thickness or non-flat surfaceprofile. One skilled in the art will recognize that a thin flexibleworkpiece of specified geometry and material and specified boundarycondition are all that is necessary to obtain a contour for the desiredloading condition of the workpiece consistent with the invention.Various other changes and modifications will be recognized to besimilarly closely related to the subject matter of the invention whichshould be defined in view of the appended claims.

What is claimed is:
 1. Apparatus for removal of heat from a planararticle under irradiation by a radiation source, said apparatuscomprising:heat sink means for removal of heat transferred thereto fromsaid article, said heat sink means including a nonplanar, nonsphericalconvex contact surface; and clamping means for securing a peripheralportion of said planar article to said contact surface such that saidarticle conforms to said contact surface, said contact surface having acontour which cooperates with said clamping means to impose uniformityof contact pressure over the surface area of said article in contactwith said contact surface and to stress said article to approach thelimiting elastic stress thereof.
 2. The apparatus of claim 1 whereinsaid article is a disc of radius r_(o) and thickness t, said peripheralportion comprises a narrow continuous region at the periphery of saiddisc, and said contour has the general mathematical form ##EQU7## whereα and β are constants, y_(max) is the maximum deflection of the disc andy is the elevation of said contour from the radial plane at the radialcoordinate r.
 3. The apparatus as defined in claim 2 wherein said disccomprises a semiconductor wafer.
 4. The apparatus of claim 2 whereinsaid clamping means cooperates with said contact surface to produce atensile stress component at the outer convex surface of said disc whichapproaches the elastic limit.
 5. The apparatus of claim 4 wherein thequantity α is given by ##EQU8## and the quantity β is given by ##EQU9##where ν is Poisson's ratio for said planar article.
 6. Apparatus fortransfer of thermal energy with a thin, flexible workpiece in vacuumcomprising:a thermally conductive member for transfer of thermal energyto or from said workpiece, said member including a nonplanar,nonspherical contact surface; and clamping means for securing aperipheral portion of said workpiece to said contact surface such thatsaid workpiece conforms to said contact surface, said contact surfacehaving a contour which is selected to cooperate with said clamping meansto impose uniformity of contact pressure over the surface area of saidworkpiece in contact with said contact surface and to stress saidworkpiece to approach the limiting elastic stress thereof, the selectionof said contour being based on the geometry and material of saidworkpiece and the forces imposed upon said workpiece by said clampingmeans.
 7. The apparatus of claim 6 wherein said clamping meanscooperates with said contact surface to produce a tensile stresscomponent at the outer surface of said workpiece which approaches theelastic limit.
 8. The apparatus of claim 6 wherein said workpiece is adisc of radius r_(o), said peripheral portion comprises a narrowcontinuous region at the periphery of said disc, and said contour hasthe general mathematical form ##EQU10## where α and β are constants,y_(max) is the maximum deflection of the disc and y is the elevation ofsaid contour from the radial plane at the radial coordinate r.
 9. Theapparatus as defined in claim 8 wherein said disc comprises asemiconductor wafer.
 10. The apparatus as defined in claim 9 furtherincludingan ion source and means for directing an ion beam from said ionsource to said semiconductor wafer and a vacuum chamber enclosing saidion source, said means for directing an ion beam, said thermallyconductive member and said clamping means, said thermally conductivemember comprising a heat sink for removal of heat from saidsemiconductor wafer during irradiation by said ion beam.